Is it the event horizon or the singularity that it takes a long time to reach. Since there would be no black holes if this effect applied at the event horizon, my guess is that it must be the singularity.

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For those inclined to oppose human meddling with the structure of the universe or the composition and configuration of objects and groups of objects within the universe, consider:
Whether there is a limit to the magnitude of a modulation of chaos below which order remains invariant? Or, is order but a fiction invented by perspectives applied over finite, however large, time intervals?